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-BARSIC- [3]
3 years ago
13

A nonzero polynomial with rational coefficients has all of the numbers [1 sqrt{2}, ; 2 sqrt{3}, ;3 sqrt{4},; dots, ;1000 sqrt{10

01}]as roots. What is the smallest possible degree of such a polynomial?
Mathematics
1 answer:
Colt1911 [192]3 years ago
8 0

Answer:

Its degree can be at least 1970

Step-by-step explanation:

for each root of the form √q, where q is not a square, we have a root -√q. Therefore, we need to find, among the numbers below to 1000, how many sqaures there are.

Since √1000 = 31.6, we have a total of 30 squares:

2², 3², 4², ...., 30², 31²

Each square gives one root and the non squares (there are 1000-30 = 970 of them) gives 2 roots (one for them and one for the opposite). Hence the smallest degree a rational polynomial can have is

970*2 + 30 = 1970

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svlad2 [7]
D because one thousand nine hundred twenty divided by 8 equals two hundred and forty
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2 years ago
Read 2 more answers
For brainiest:):):):):):):):)
mars1129 [50]

Answer:

A1) 125

A2) 47.5%

B) 30

Step-by-step explanation:

Remember 'of' in this sentence means times(*). % shows a certain number/100.

a1) 48% 'of' what number is 60?

(let unknown number be x)

48/100 *x=60

Solve the equation, and the answer is x=125

a2) what percentage 'of' 120 is 57?

(let the unknown percentage be x)

(x/100)*120=57

x=47.5%

b) 24 students= 80% of the total number of students

1%=24/80

100% of the total number of students=30

So, there are total of 30 students

8 0
2 years ago
Hey can you please help me posted picture of question
fenix001 [56]
The summary of directions of the parabola is:

a) Squared term is x
Parabola either opens up or down.
Positive coefficient means upward opening and negative coefficient means downward opening

b) Squared term is y
Parabola either opens right or left
Positive coefficient means rightwards opening and negative coefficient means leftwards opening

Since the coefficient is positive with squared x term, the parabola opens upward.

So the answer to this question is option D
4 0
3 years ago
The length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, wo
andrew11 [14]

Answer:

<em>24 children</em>

Step-by-step explanation:

If the length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, this is represented as;

y  \alpha \frac{1}{x}\\y =\frac{k}{x}

k is the constant of proportionality

If it takes 16 children 6 hours to put the jigsaw puzzle together, this means at x = 16, y = 6

Substitute:

6 = k/16

k = 6*16

k = 96

W are to find number of children needed to put the same jigsaw puzzle together in 4 hours, this is done by substituting k = 96 and y = 4 into the expression y = k/x

y = 96/4

y = 24

<em>Hence it will take 24 children to put the same jigsaw puzzle together in 4 hours</em>

<em></em>

5 0
3 years ago
How do you simplify 2^6? What do you get?
sertanlavr [38]

Answer:

64

Step-by-step explanation:

2*2*2*2*2*2

2 multiply 2 multiply 2 multiply 2 multiply 2 multiply 2.

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2 years ago
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